SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Surface area of 3D shapes(sphere, prism, cylinder)

Grade: 4-a Lesson: S3-L2

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

The cylinder has a surface area of 596.6 inches and a radius of 5 inches. Find its height.(π = 3.14)

Step 1a

Given that the surface area (A) is 596.6 inches and the radius (r) is 5 inches, find the height (h).

The formula gives the surface area (A) of a cylinder : \$A = 2πr^2 + 2πrh\$

$1a$

Explanation: In this stage, determine the height (h) of a cylinder with a surface area (A) of 596.6 inches and a radius (r) of 5 inches using the formula \$A = 2πr^2 + 2πrh\$.

Step 1b

Now plug the values into the formula: 596.6 = \$2(3.14)(5)^2 + 2(3.14)(5)h\$

596.6 = \$157 + 31.4h\$

Explanation: In this step, substitute the given values into the equation: 596.6 equals 2 times the area of the base plus 2 times the product of pi, the radius, and the height.

Step 1c

To isolate h, need to subtract 157 from both sides of the equation:

596.6 - 157 = 157 - 157 + 31.4h

h = \$439.6/31.4\$

h = 14

So, the height of the cylinder is 14 inches.

Explanation: In this stage, to isolate h, subtract 157 from both sides: 596.6 - 157 = 157 - 157 + 31.4h. Solve for h : h =

\$439.6/31.4\$, yielding a height of 14 inches for the cylinder.